Optical frequency measurement and control using dual optical-frequency combs

Abstract

A dual-comb optical-frequency comb generator includes a tunable comb-generating laser, a coarse-comb generator, a fine-comb generator, a second harmonic generator, a coarse-comb offset photodetector, a dual-comb offset photodetector, and a fine-comb photodetector. The coarse comb is self-referencing and coupled to the fine comb so as to enable absolute determination of the frequencies of the fine comb.

What is claimed is: 
     
       1. An apparatus comprising:
 (a) a tunable comb-generating laser that generates a comb-generating laser signal at an optical frequency ν p ; 
 (b) a coarse-comb generator structured and arranged so as to receive a first portion of the comb-generating laser signal and to generate therefrom a coarse optical-frequency comb having optical frequencies ν N =ν p +NΔ where N is an integer and Δ is a coarse-comb frequency spacing, wherein the coarse optical-frequency comb spans at least an octave of optical frequency; 
 (c) a fine-comb generator structured and arranged so as to receive a second portion of the comb-generating laser signal and to generate therefrom a fine optical-frequency comb having optical frequencies ν N′ =ν p +N′Δ′ where N′ is an integer and Δ′ is a fine-comb frequency spacing; 
 (d) a second harmonic generator structured and arranged so as to (i) receive at least a portion of the coarse optical-frequency comb, including a comb optical signals at an optical frequency ν N1 , and (ii) generate from the comb optical signal at ν N1  a second harmonic optical signal at an optical frequency 2ν N1 ; 
 (e) a coarse-comb offset photodetector structured and arranged so as to (i) receive the second harmonic optical signal, (ii) receive at least a portion of the coarse optical-frequency comb, including a comb optical signal at an optical frequency ν N2 ≈2ν N1 , and (iii) generate, from the comb optical signal at ν N2  and the second harmonic optical signal at 2ν N1 , a coarse-comb offset electrical signal at a coarse-comb offset frequency f 0 =|2ν N1 −ν N2 |; 
 (f) a dual-comb offset photodetector structured and arranged so as to (i) receive at least portions of the coarse and fine optical-frequency combs, including comb optical signals at optical frequencies ν p +Δ and ν p +MΔ′, or ν p −Δ and ν p −MΔ′, where M is a positive integer closest to Δ/Δ′, and (ii) generate from the comb optical signals a dual-comb offset electrical signal at a dual-comb offset frequency f 1 =|Δ−MΔ′|; and 
 (g) a fine-comb photodetector structured and arranged so as to (i) receive at least portions of the fine optical-frequency comb, and (ii) generate from the fine optical-frequency comb a fine-comb-spacing electrical signal at the fine-comb frequency spacing Δ′. 
 
     
     
       2. The apparatus of  claim 1  further comprising one or more electronic processors or circuit elements structured, connected or programmed so as to determine the optical frequency ν p  using measured values of Δ′, f 0 , and f 1 . 
     
     
       3. The apparatus of  claim 1  further comprising:
 (H) a tunable output laser that generates an output laser signal at an output optical frequency ν OUT ; and 
 (I) an output offset photodetector structured and arranged so as to (i) receive at least a portion of the fine optical-frequency comb at an optical frequency ν N′  and at least a portion of the output laser signal, and (ii) generate, from the received portion of the fine optical-frequency comb at the optical frequency ν N′  and the received portion of the output laser signal, an output offset electrical signal at an output offset frequency f 2 =|ν OUT −ν N′ |. 
 
     
     
       4. The apparatus of  claim 3  further comprising a coarse-comb servo controller coupled to the coarse-comb generator and a fine-comb servo controller coupled to the fine-comb generator, wherein (i) the fine-comb servo controller is structured and connected so as to control Δ′ based on an error signal that is a difference between Δ′ and a frequency f FCR  of a fine-comb reference electrical signal, and (ii) the coarse-comb servo controller is structured and connected so as to control Δ based on an error signal that is a difference between f 1  and a frequency f CCR  of a coarse-comb reference electrical signal. 
     
     
       5. The apparatus of  claim 4  further comprising an electronic frequency source structured, arranged, and connected so as to generate one or both of the reference electrical signals at the frequencies f FCR  or f CCR  using one or more of a reference oscillator, an atomic transition, direct digital synthesis, or harmonic frequency multiplication. 
     
     
       6. The apparatus of  claim 3  further comprising a coarse-comb-offset servo controller coupled to the comb-generating laser, the coarse-comb-offset servo controller is structured and connected so as to control ν p  based on an error signal that is a difference between f 0  and a frequency f OFFR  of a coarse-comb-offset reference electrical signal. 
     
     
       7. The apparatus of  claim 6  further comprising an electronic frequency source structured, arranged, and connected so as to generate the reference electrical signal at the frequency f OFFR  using one or more of a reference oscillator, an atomic transition, direct digital synthesis, or harmonic frequency multiplication. 
     
     
       8. The laser source of  claim 3  further comprising one or more electronic processors or circuit elements structured, connected or programmed so as to determine the optical output frequency ν OUT  using measured values of Δ′, f 0 , f 1 , and f 2 . 
     
     
       9. The laser source of  claim 3  further comprising a laser output servo controller coupled to the output laser, wherein the laser output servo controller is structured and connected so as to control ν OUT  based on an error signal that is a difference between f 2  and a frequency f LOR  of a laser-output reference electrical signal. 
     
     
       10. The laser source of  claim 9  wherein the laser output servo controller is structured and connected to tune the optical output frequency ν OUT  in response to tuning of f LOR . 
     
     
       11. The laser source of  claim 10  wherein (i) the laser source further comprises one or more corresponding servo controllers coupled to one or more of the comb-generating laser, the coarse-comb generator, or the fine-comb generator for maintaining one or more of f 0 , f 1 , or Δ′, respectively, substantially constant at corresponding selected values, and (ii) the laser output servo controller is structured and connected to tune the optical output frequency ν OUT  to a selected output optical frequency ν SEL , or maintain ν OUT  at ν SEL , in response to tuning or control of f LOR  according to a calibrated dependence of ν OUT  on f LOR  for the selected values of one or more of f 0 , f 1 , or Δ′. 
     
     
       12. The apparatus of  claim 9  wherein (i) the coarse-comb generator comprises a first optical resonator, and the coarse-comb servo controller is structured and connected to effect control of Δ by thermal tuning of the first optical resonator, or (ii) the fine-comb generator comprises a second optical resonator, and the fine-comb servo controller is structured and connected to effect control of Δ′ by thermal tuning of the second optical resonator. 
     
     
       13. The apparatus of  claim 12  wherein (i) thermal tuning of the first optical resonator is effected by controlling a first optical amplifier arranged to control a power level of the first portion of the comb-generating laser signal, or (ii) thermal tuning of the second optical resonator is effected by controlling a second optical amplifier arranged to control a power level of the second portion of the comb-generating laser signal. 
     
     
       14. The laser source of  claim 9  further comprising an electronic frequency source structured, arranged, and connected so as to generate the laser-output reference electrical signal at the frequency f LOR  using one or more of a reference oscillator, an atomic transition, direct digital synthesis, or harmonic frequency multiplication. 
     
     
       15. The apparatus of  claim 3  wherein one or both of the comb-generating laser or the output laser are tunable semiconductor lasers on a substrate. 
     
     
       16. The apparatus of  claim 15  wherein the comb-generating laser or the output laser includes two or more ring optical resonators coupled thereto and arranged so as to effect tuning of the corresponding laser by tuning of respective reflectance spectra of the coupled ring optical resonators. 
     
     
       17. The apparatus of  claim 3  wherein the coarse-comb and fine-comb generators are structured and arranged so that each one of f 0 , f 1 , and Δ′ is less than about 25 GHz. 
     
     
       18. The apparatus of  claim 3  wherein (i) the coarse-comb generator comprises a first optical resonator, or (ii) the fine-comb generator comprises a second optical resonator. 
     
     
       19. The apparatus of  claim 18  wherein the first or second optical resonator comprises a disk, microdisk, ring, or microring resonator on a substrate. 
     
     
       20. The apparatus of  claim 19  wherein the substrate comprises one or more semiconductors, and the first or second optical resonator comprises one or more semiconductors, one or more metal or semiconductor oxides, one or more metal or semiconductor nitrides, or one or more metal or semiconductor oxynitrides. 
     
     
       21. The apparatus of  claim 3  wherein ν p  is between about 100 THz and about 800 THz, Δ is between about 0.2 THz and about 10 THz, and Δ′ is between about 1.0 GHz and about 100 GHz. 
     
     
       22. The apparatus of  claim 3  wherein ν p  is between about 180 THz and about 200 THz, Δ is between about 0.5 THz and about 2 THz, and Δ′ is between about 5 GHz and about 20 GHz. 
     
     
       23. The apparatus of  claim 3  wherein the fine-comb generator comprises a modelocked laser having a pulse repetition frequency about equal to Δ′ or a phase modulator sideband generator operated at a modulation frequency about equal to Δ′. 
     
     
       24. The apparatus of  claim 3  wherein the second harmonic generator includes one or more nonlinear optical materials including one or more crystalline materials, one or more periodically poled materials, one or more thin film materials, or one or more nonlinear optical materials incorporated into a waveguide. 
     
     
       25. The apparatus of  claim 24  wherein the second harmonic generator includes a periodically poled lithium niobate film on a silicon nitride waveguide on a silicon substrate. 
     
     
       26. The apparatus of  claim 3  wherein each one of the photodetectors comprises a waveguide photodiode on a substrate. 
     
     
       27. The apparatus of  claim 3  wherein the comb-generating laser, the coarse-comb generator, the fine-comb generator, the second harmonic generator, each photodetector, and the output laser are integrated onto a common substrate. 
     
     
       28. The apparatus of  claim 27  wherein one or more electronic processors or circuit elements are integrated onto the common substrate.